4.8k views
3 votes
If the y-intercept moved up or down and how
muchf(x)= x and g(x) = 3f(x):

User David Culp
by
8.5k points

1 Answer

4 votes

Final answer:

When the function f(x) = x is scaled to become g(x) = 3f(x), the slope is tripled, but the y-intercept remains at 0. Changing a line's y-intercept would shift the line up or down without altering the slope.

Step-by-step explanation:

The question is asking about the effect of changing the y-intercept on the graph of a function. According to the provided information, an original line with a y-intercept of 9 and a slope of 3 is described. When the function f(x) = x is multiplied by 3 to get g(x) = 3f(x), the slope is tripled, but the y-intercept does not change because f(x) passes through the origin (0,0) and thus has a y-intercept of 0 to begin with. Therefore, in the example given, the graph of g(x) will have a slope of 3 times the slope of f(x), but the y-intercept will remain the same, at the origin.

If we were to change the y-intercept of a line by some value, the line would shift up or down on the graph, maintaining the same slope. If the y-intercept is increased, the line shifts up; if it is decreased, the line shifts down. This does not affect the steepness or direction of the line, only its vertical position.

User Tshilidzi Mudau
by
8.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.